Last year in Moscow, a mundane case came before the courts; it was brought by an ageing son who was seeking the judicial rehabilitation of his father. There have been many such cases in recent years. Stalin's NKVD worked to death or executed millions of innocent Soviet citizens, and their families can now wipe the blot of shame from the official records in this way. The difference in this particular case was that the deceased had not been shot in Stalin's lifetime but some months afterwards. More remarkably, he had been someone most people regarded not as a victim but rather as a Stalinist killer: Lavrenti Beria. The case was given due consideration, but in the end the plea made by his son Sergo was rejected.

Lavrenti Beria was one of Stalin's NKVD leaders in the Great Terror, and headed the NKVD from 1938 until being transferred to oversee the Soviet nuclear bomb project. Introducing him to Churchill during the second world war, Stalin playfully described him as "our Himmler". Beria supervised the deportation of several nations in wartime and was in charge of the Katyn massacre of Polish officers. He terrified even the Red Army high commanders; the phrase they had for being purged was "going to have coffee with Beria".

Only Stalin intimidated Beria as much as Beria intimidated others. Before dying in March 1953, Stalin seems to have decided at last to get rid of him. Beria therefore had a vital interest in seeing Stalin laid into a coffin, and there were rumours that he murdered him. The scene of Stalin's death agony was grotesque. When it looked as though he was breathing his last, Beria's face shone with delight. But during those minutes when Stalin returned to consciousness, Beria got to his knees and lovingly kissed his hands.

After Stalin's funeral, Beria was the first to set about discrediting him in the eyes of the supreme communist leadership. Secret tapes of Stalin's conversations were played to the central committee. The "cult of the individual" was denounced. Beria campaigned for a basic revision of Soviet policies at home and abroad. He was in a powerful position to become the single successor, but his luck did not hold. In June 1953, his colleagues Nikita Khrushchev and Georgi Malenkov had him arrested, suspecting that he was planning a coup d'état. Having resumed control of the security agencies, he certainly had the institutional opportunity, and his career showed he had the ruthless ambition. A secret military trial followed. In December 1953, despite his pleas for forgiveness, he was shot.

Accounts of Beria have been heavily influenced by the version put out by Khrushchev, who won the struggle for the succession. Rarely was it noted that Khrushchev was hardly unbiased; he, too, had filled lakes of blood during the Great Terror. But by the mid-1950s he was in power, and covered up his past by ordering the incineration of incriminating documents. He also suppressed the fact that in the months after Stalin's death, Beria did more than anyone to change the policies and practices of the regime. It is pretty clear that Khrushchev and his friends eliminated Beria as much because his proposals threatened the stability of the state order as because he was a killer-policeman. No Soviet leader until Gorbachev would have so wide a reformist programme.

Russians understandably found it hard to accept Beria's dual nature as killer and reformer. I remember giving a paper on the subject in the 1980s, and attracting angry incredulity that anyone could say anything about him other than that he was a monster. Today, this is becoming the conventional interpretation; Russia's citizens, after years of historical revelations, are readier to believe that Beria, bad as he was, was not much worse than most of the rivals who killed him.

But Sergo Beria went much further than this. With his court case and with this memoir he has aimed to show that his father was not a monster at all, but a cultured thinker and a warm human being. He gives details about the Beria family which have never previously been disclosed. He loved his wife; according to Sergo, the story that he had abducted and raped her before their marriage was a myth. The book, brilliantly translated by Brian Pearce, claims too that Beria understood the inadequacies of Leninism, but could do nothing about the situation in the USSR until after Stalin had died. Allegedly Lavrenti Beria always strove to hinder the worst excesses of the Stalinist order and was a reluctant purger. This is clearly a work of filial piety.

This does not prevent it from being full of important information. Sergo Beria knew all the Kremlin leaders, and depicts them with a waspish wit. As a trained linguist and scientist, he attended crucial meetings such as the Yalta Conference. His portrait of life at the apex of Soviet politics - the fears, the pace of work, the recreations, the dinner parties - is more vivid than anything that has yet appeared. On political decisions he is less reliable. Often he did not know what was really going on, and anyway he is heavily biased in his father's favour.

But the book makes for compulsive reading. Not many young men were courted by Stalin's daughter - and had the nerve to turn her down. Sergo witnessed extraordinary scenes in the Kremlin and at home. Once his mother, Nina, was insulted by a drunken actor in Stalin's presence. She scolded Stalin for failing to defend her. Stalin walked across to console her. "Nina," he said, "this is the first time I have kissed a woman's hand." That night Nina told off her husband too, complaining that he had overlooked the actor's insult. No one else made both Stalin and Beria cringe. Sergo Beria's memoir does not and cannot plausibly rehabilitate his father, but as a record of the private lives of Stalin's murderous elite it has no rival.

 Robert Service's Russia: Experiment With a People will be published by Palgrave next year. His Lenin: A Biography is available in paperback.